Arsenal launched their Champions League escapology act with a famous victory against Bayern Munich.

Arsene Wenger hailed it a tactical triumph and applauded his team's 'discipline' and 'mental strength' as he challenged his players to believe they belong in this elite company.

The German champions had won their previous 12 games in all competitions but could not find a way through Wenger's well-organised defensive unit in a thrilling encounter.

Arsene Wenger has urged his side to believe following their 2-0 Champions League defeat of Bayern Munich

Arsenal players race to celebrate with Olivier Giroud (centre) after the Frenchman opens the scoring

Mesut Ozil capped a memorable victory with Arsenal's second goal, scored in stoppage time

A happy Ozil posted this picture on Instagram after putting the final touch on Arsenal's win over Bayern

Olivier Giroud headed the Londoners into the lead following an uncharacteristic blunder by Bayern goalkeeper Manuel Neuer and Mesut Ozil grabbed a second in stoppage time.

Arsenal moved into third place in Group F and still have work to do but the manager is confident they are improving fast.

'We had an absolute necessity to win and we did it in intense disciplined game,' said Wenger. 'We stopped them from playing. When they opened us up I dropped Ozil deeper to make it tight and catch them on the break.

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'In the final part of the game, when we went longer, they struggled. They dropped a bit physically as well. Overall we have beaten a very strong team, with our strong level of focus and a clean sheet.

'It can strengthen our belief and the belief of our fans. We have won 3-0 against Man United, we won 3-0 at Watford and 2-0 against Bayern.'

Wenger praised Petr Cech for a series of fine saves but ducked the question of whether it was a mistake to rest his No.1 goalkeeper in the last game, when Arsenal were beaten at home by Olympiakos.

'I was expecting that question,' he replied. 'Petr Cech kept us in the game and you can say the same about Neuer.'

Petr Cech made a succession of fine saves after being recalled to the Champions League starting line up

Wenger credited the former Chelsea keeper for keeping his side in the game at the Emirates

GROUP F REMAINING FIXTURES

November 4 Bayern Munich vs Arsenal

Olympiacos vs Dinamo Zagreb

November 24 Arsenal vs Dinamo Zagreb

Bayern Munich vs Olympiacos

December 9 Dinamo Zagreb vs Bayern Munich

Olympiacos vs Arsenal

The Arsenal boss was keen to offer credit to Giroud, who has lost his place in the team to Theo Walcott but came off the bench to score the vital opener, in the 77the minute.

'It is not easy, because he has always played,' said Wenger. 'He had a little dip in form but he is coming back to his best. He's a winner, and when it doesn' t work for us on the ground, he gives us options in the air.'

Giroud scored with an untidy combination of his face and his hand as Neuer missed a free-kick taken by Santi Cazorla.

'It is certainly not my most beautiful goal but it's one of the most important,' said Giroud. 'I just needed a helping hand from destiny. It worked in my favour.

'It shows that we kept believing until the end and this shows our mental strength to stand up to our opponents and to play on the counterattack. I think we did that rather well tonight.'

Pep Guardiola was proud of his team despite Bayern Munich slipping to their first competitive defeat this term

Guardiola refused to blame Manuel Neuer (centre) for his decision that led to Arsenal's opening goal

Bayern dominated possession and manager Pep Guardiola refused to pin the blame on Neuer, who made a fabulous save from Walcott in the first half.

'In the first half he made great saves,' said Guardiola. 'Never in my life have I criticised a player for taking decisions, correct or not correct. We did not lose because of Manuel Neuer. He took a decision in that situation and that's it.

'I'm so proud of my team. I like to win. I'm not happy but we played with courage, to come here and take the ball from Arsenal's players. I can't explain why we didn't score. It's mystery.'